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Spherically symmetric solutions admitting a homothetic Killing vector field(HKVF) either orthogonal, $\eta_{\bot}$, or parallel,$\eta_{||}$, to the4-velocity vector field, $u^a$, are studied. New self-similar solution ofEinstein's field equation is found in the case when HKVF is in a general form.Some physical properties of the obtained solution are examined.

On Spherically Symmetric Non-Static Space-Times Admitting Homothetic Motions